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Zeitschrift für Analysis und ihre Anwendungen

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Volume 15, Issue 2, 1996, pp. 275–278
DOI: 10.4171/ZAA/698

Published online: 1996-06-30

A Note on the Bonnet-Myers Theorem

V. Boju[1] and Louis Funar[2]

(1) Universitatea din Craiova, Romania
(2) Université Grenoble I, Saint-Martin-d'Hères, France

The aim of this note is to derive a compactness result for complete manifolds whose Ricci curvature is bounded from below. The classical result, usually stated as Bonnet-Myers theorem, provides an estimation of the diameter of a manifold whose Ricci curvature is greater than a strictly positive constant. Weaker assumptions that the Ricci curvature function tends slowly to zero (when the distance from a fixed point goes to infinity) were already considered in [2, 3]. We shall improve here their results.

Keywords: Ricci curvature, Jacobi equation

Boju V., Funar Louis: A Note on the Bonnet-Myers Theorem. Z. Anal. Anwend. 15 (1996), 275-278. doi: 10.4171/ZAA/698